Wednesday, May 28, 2008
Countably Distinct and Yet Not Countably Distinct
In Cyrano de Bergerac, Roxane falls in love with a man who is beautiful, brilliant, and brave. His beauty is Christian's, his brilliance is Cyrano's, and his bravery belongs to both. Roxane, of course, does not know that Christian and Cyrano are two different people, and she has no way of knowing. Therefore, insofar as they are the object of Roxane's love, the two are not countably distinct -- they both together are one object of Roxane's love, and she is not wrong when she says toward the end, after they are dead and she has found out, that she only loved one man but lost him to death twice. It's not the case that she really loves Christian, and not Cyrano; or that she really loves Cyrano, and not Christian; she loves them both as one man. And therein lies the tragedy: Christian and Cyrano are not countably distinct insofar as she knows and loves them, but they are insofar as they are persons in their own right. It's quite the tragic tangle: Christian is not identical to Cyrano, neither is identical to the man Roxane loves, but in terms of the unit of counting 'men whom Roxane loves', they are all indistinct: Roxane has no way to count Christian differently from Cyrano, or either from the man she loves; they are one man whom Roxane loves. But change the unit of counting and they fall apart: Christian is a distinct man, and Cyrano is a second distinct man, and the 'man whom Roxane loves' is not a distinct man at all but two men whom she cannot distinguish from each other. To be overtechnical about it: countable unity is sortal-relative; whether something counts as one depends on your units of counting.